Defining parameters
Level: | \( N \) | = | \( 169 = 13^{2} \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(18928\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(169))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8395 | 8286 | 109 |
Cusp forms | 8167 | 8081 | 86 |
Eisenstein series | 228 | 205 | 23 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(169))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
169.8.a | \(\chi_{169}(1, \cdot)\) | 169.8.a.a | 1 | 1 |
169.8.a.b | 2 | |||
169.8.a.c | 4 | |||
169.8.a.d | 6 | |||
169.8.a.e | 8 | |||
169.8.a.f | 8 | |||
169.8.a.g | 14 | |||
169.8.a.h | 21 | |||
169.8.a.i | 21 | |||
169.8.b | \(\chi_{169}(168, \cdot)\) | 169.8.b.a | 2 | 1 |
169.8.b.b | 4 | |||
169.8.b.c | 8 | |||
169.8.b.d | 14 | |||
169.8.b.e | 16 | |||
169.8.b.f | 42 | |||
169.8.c | \(\chi_{169}(22, \cdot)\) | n/a | 168 | 2 |
169.8.e | \(\chi_{169}(23, \cdot)\) | n/a | 170 | 2 |
169.8.g | \(\chi_{169}(14, \cdot)\) | n/a | 1260 | 12 |
169.8.h | \(\chi_{169}(12, \cdot)\) | n/a | 1248 | 12 |
169.8.i | \(\chi_{169}(3, \cdot)\) | n/a | 2544 | 24 |
169.8.k | \(\chi_{169}(4, \cdot)\) | n/a | 2520 | 24 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 1}\)